"I've got to do something useful while I'm here," the tourist from Arizona muttered. "I read that Bush is in Vegas this morning, and I almost went over to hear him. But I think he's way across town."

Of course, if Goldenson wanted to see a presidential candidate in this city, he didn't have to travel that far. The same morning last week when President Bush was speaking at the University of Nevada at Las Vegas, John F. Kerry was campaigning barely a block from the casino where Goldenson was losing his money. First lady Laura Bush was stumping on the Vegas strip the same day. And Teresa Heinz Kerry was also in Nevada, at a Democratic rally in Reno.

By traditional rules, it would seem crazy for the campaigns to put that much firepower into a state with just five electoral votes less than three weeks before Election Day. But the 2004 election is so close, and the remaining battleground states so few, that Nevada and its southwest neighbors have become prime targets for both campaigns.

Of the five states in the "Cactus Corridor" of the desert Southwest, only one -- Utah, a Republican stronghold -- seems firmly decided. Arizona, where polls showed a dead heat at the end of the summer, moved strongly to Bush in September, but the Democrats now say they are clawing back. Nevada, New Mexico and Colorado all appear to be up for grabs.

As a result, the major candidates have been constant visitors this fall to a region that barely saw any presidential campaigning four years ago. In the past two weeks, the presidential contenders and their running mates have been to Denver and Colorado Springs, Albuquerque and Santa Fe, Reno and Las Vegas, Phoenix and Tempe.

But they have also found time to campaign in the oil-patch hamlet of Hobbs, N.M., in the desert town of Henderson, Nev., and in the shopping-mall suburb of Commerce City, Colo.

In demographic terms, it makes sense for the candidates to move toward the Southwest, because millions of voters have moved in this direction in recent years. The four southwest battleground states gained five electoral votes since the 2000 election. If either candidate could sweep Arizona, Colorado, Nevada and New Mexico, the total of 29 electoral votes would be a bigger prize than Florida.

Much of the in-migration has been low-income workers, particularly Hispanic, coming for jobs in the tourism industry -- hotel maids, ski lift attendants -- that tend to pay close to the minimum wage. Organizations such as Moving America Forward, a creation of New Mexico Gov. Bill Richardson (D), have been energetically registering these newcomers to vote.

The result has been particularly dramatic in Nevada. Republicans here had a 14,000-vote advantage in registered voters in January. When registration closed on Oct. 12, preliminary registration figures showed that Democrats had pulled even or perhaps slightly ahead. Normally, new registrants turn out in large numbers for their first election.

There has also been a push to sign up new voters on Indian reservations, where the vote tends to be strongly Democratic. Indian turnout is expected to increase significantly in New Mexico and Arizona because the Navajo Nation, with 300,000 voters, has scheduled its tribal election this year for Nov. 2, the same day as the presidential vote.

Still, the Democrats are playing catch-up in a region that had been largely Republican. In the 2000 election, Bush carried Arizona, Nevada and Colorado comfortably with minimal personal campaigning; he lost New Mexico by a smidgen.

Republican leaders say the established voting pattern will reemerge on Election Day.

"Yes, we've got a close race this year," says Colorado Gov. Bill Owens, a strong Bush ally. "But I expect we're going to see the Republicans come home when it's time to vote. The polls show that is already happening in Arizona. I think we'll see the same thing in Colorado. And the president is personally popular in New Mexico, which probably explains why we're running even there."